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Today's Topics:

  1. Re: How to define an operator A in "models.xml" (Matthias Troyer)
  2. multiple eigenvalues (degenerate eigenstates) in  sparsediag
     (Andriy Zhugayevych)


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Message: 1
Date: Thu, 24 Mar 2011 12:28:28 -0500
From: Matthias Troyer <troyer@phys.ethz.ch>
Subject: Re: [ALPS-users] How to define an operator A in "models.xml"
To: comp-phys-alps-users@lists.phys.ethz.ch
Message-ID: <DAC79DA4-5BC5-49DA-BAAE-1B885B6736BB@phys.ethz.ch>
Content-Type: text/plain; charset="utf-8"

Dear Sunzhaoyu,

This is not implemented yet. For now you will have to decompose it into more elementary operators.

Matthias

On Mar 18, 2011, at 12:38 AM, ??? wrote:

> Dear ALPS users and developers
>
> I want to re-produce the result of a 12x2 spin ladder with four-site interaction.
> The four-site interaction is between two nearest-neighboring rungs.
> Please see:
> [    Phys. Rev. B 74, 155119 (2006),  http://prb.aps.org/abstract/PRB/v74/i15/e155119     ]
>
>
> However, it seems that ALPS 2.0 do not support 4-site terms.
> Thus I define every rung  as a single site,
> then the ladder becomes a one-dimensional chain (local degree of freedom is 4),
> and the four-site interaction becomes a two-site interaction.
>
> In original ladder, the SITEBASIS is just  {sz} = {-1/2, 1/2}.
> In this basis operators such as Sminus have very compact expressions
> thus they can be simply define as:
>   <OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))">
>
>
> However, in the new model, a possible choice of SITEBASIS  is {J,Jz}={00, 1-1, 10, 11}.
> In this new basis, operators do not have  very compact expressions,
> however, the elements of the operator  can be easily obtained  through unitary transformation.
> The problem is, I can figure out all the elements of an operator in basis{J, Jz}, but I do not know how to define the operator in "models.xml".
>
> In other words,
> suppose an operator X in basis {J, Jz} is explicitly found to be
> [ 1, 0, 0, 0
>   0, 2, 1, 0
>   0, 1, 3, 0
>   0, 0, 0, 4]
> then in ALPS 2.0, is it possible to define X by simply writing down every elements Xij  in "models.xml" ?
>
> Any suggestion would be appreciated.
>
>
> sunzhaoyu
>
>
>
>
>
>
>
>
>

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Message: 2
Date: Thu, 24 Mar 2011 19:26:00 -0500
From: "Andriy Zhugayevych" <azh@ukr.net>
Subject: [ALPS-users] multiple eigenvalues (degenerate eigenstates) in
       sparsediag
To: <comp-phys-alps-users@lists.phys.ethz.ch>
Message-ID: <8FAAAF26EE22499C8C35D5CBE4FAA101@dv5t1200se>
Content-Type: text/plain; format=flowed; charset="koi8-r";
       reply-type=original

For a system with multiple eigenvalues (e.g. ground state of the extended
Hubbard model on a closed chain of 4 sites with 4 electrons, zero spin, and
U=2V) sparsediag program returns only one eigenstate for each multiplet. How
other eigenstates can be obtained if there is no quantum number
differentiating them?

Thanks,
Andriy



End of Comp-phys-alps-users Digest, Vol 60, Issue 16
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